Tuned mass systems have been used for more than a century to mitigate undesirable dynamic responses of a primary system. A standard tuned mass damper (TMD) is a device consisting of a mass, a spring, and a damper that is attached to a structure in order to reduce the dynamic response of the structure. The frequency of the TMD is tuned to a particular structural frequency so that when that structural frequency is excited, the damper will resonate. Energy is dissipated by the inertial force of the TMD acting on the structure.
FIG. 1 represents a traditional prior art TMD system 10, where M1 represent a primary bulk mass. The bulk mass M1 vibrates when excited acting on spring K1 and damper C1. M2 is a secondary reaction mass (mitigating mass), K2 is a reaction mass spring rate, and C2 is a secondary damper. The TMD system 10 utilizes the resonant condition of the mitigating mass M2 to provide a means to dissipate energy out of the entire system. A drawback to current TMD systems is that they are a “responsive” approach to mitigating excitation. “Responsive” in this context means that their effectivity is directly dependent upon responding to the force input's frequency and amplitude. It takes time to transfer and dissipate the energy from the primary system M1 into the mitigating mass M2. During this transfer rise time, the primary system response is minimally mitigated.
The prior art TMD systems approach focuses on the transfer and dissipation of energy. There is an undesirable vibration condition that the systems are designed to mitigate and since most passive energy dissipation techniques rely upon velocity or displacement there is significant nonlinearity of the mitigated response to various input frequencies and amplitudes. TMDs tend to work well at a single vibration amplitude. For example, if the TMD functions well at medium vibration amplitude then it does not work as well at small or large vibration amplitudes due to the nonlinear characteristics of the standard C2 damping mechanism. A system and method that does not rely on responsive damping, and that provides a linear and force independent mitigation of excitation, is desired.
Another drawback, that is inherent with nonlinear characteristics of the standard C2 damping mechanism, is frequency sensitivity. The velocity of the flow pumping through the C2 mechanisms is different at various frequencies. For example the velocity traveling across a C2 loss mechanism at 5 Hz is half of the velocity at 10 Hz. Since the typical TMD C2 mechanism is to incorporate a viscous or columb device, the maximum energy dissipation can only occur at a specific frequency. Any other frequency will cause a different flow rate through C2 and therefore different loss coefficient. This is why TMD performance, which relies upon the resonant response of the M2 system, is highly sensitive to accuracy of tuning. The flow rate through the C2 changes drastically depending upon how well the M2 reaction system is tuned to the primary system. Therefore, an additional significant drawback of current TMD systems is their limitation to only effectively mitigate over a highly narrow frequency range.
A standard TMD is typically optimized by adjusting the reaction mass suspension stiffness (K2) and damping (C2) to maximize vibration mitigation. Adjustment of the K2 term is not difficult. The C2 term, on the other hand, can dramatically impair TMD attenuation performance if it is not carefully configured for the specific vibration amplitude and frequency.
A similar damping system known as a Tuned Vibration Absorber (TVA) utilizes the mitigating mass as a counter inertia/force mechanism. TVA systems typically have the same drawbacks as TMD systems, e.g., response time, nonlinearity, and narrowband response. With both the TVA and TMD approaches, energy has to be placed into the TVA or TMD system to mitigate response.
A system and method according to the present overcomes these multiple drawbacks by providing a resistance-to-motion controlled coupling mechanism that replaces prior art C2 dampers in the prior art TMD systems. It is this method and described system that fundamentally alters the primary system response by setting new modal gain system attributes and eliminates frequency tuning sensitivity. The resistance-to-motion controlled coupling mechanism does not dampen vibration in a responsive manner, as taught by resistance-to-motion mechanisms in the prior art, but rather changes the fundamental characteristics of the system by mandating allowable phase of participation between the masses. In other words the system dictates allowable coupling to set complex modeshape and gain.
Prior art methods are “responsive” in nature and generally require a transfer of energy into the secondary mass (M2) so the secondary mass responds and can either provide a counter inertia force (TVA) or provide a means to bleed energy out of the system (TMD). In contrast, the system according to the present disclosure is “transformative” in nature. It does not attempt to dissipate energy, but rather dictates the allowable phase of participation between the primary mass M1 and the secondary mass M2 with the resistance-to-motion controlled coupling C2 mechanism providing the desired resistance to the primary mass M1. Constant resistance will provide a constant phase of participation between the masses. Varying resistance will result in a corresponding varying of phase of participation between the masses. Each resistance level and its resulting phase of participation establishes a unique modal gain characteristic of the coupled system. A desired modal gain response is achievable by prescribing a resistance profile to any given force.
The current art provides the means to dictate the allowable participation between masses to set the fundamental modal gain response characteristics of a coupled system. Unlike the prior art systems, frequency matching between the primary system and sprung secondary system is not required to achieve this disruptive altering of modal characteristics. The same effectiveness as the prior art is achieved by simply dictating the phase of participation between masses wherever the sprung secondary system has modal mass participation in the combined system responses. I.e. not at a node point.
Historically, analysis of the C2 damping component of the TMD system has focused almost entirely upon the dissipation of energy. The objective of the TMD to date has been to bleed energy from the vibrating M2 component into the C2 dissipative component. While this approach can be used to generate a TMD design that mitigates vibration, the approach provides a nonlinear vibration mitigation methodology. The proposed method of controlling and managing the phase relationship between M1 and M2 independent of vibration amplitude produces a vibration mitigation device that significantly outperforms all previous TMD designs.
Modern TMD C2 damping mechanisms rely on flow of fluid or gas through an orifice to function. The C2 damping mechanism provides a “resistance to motion” between M1 and M2. The orifice based approach is characterized by a velocity squared (V2) relationship between C2 force and relative velocity. This non-linear squared relationship generates a vibration mitigation approach that is only optimized for a singular vibration amplitude or excitation force. The non-linear relationship of the orifice based TMD system yields a dynamic mitigation mechanism that performs differently at low, medium, and high vibration amplitudes.
FIG. 1b shows the three dimensional Frequency Response Function FRF characteristics of the standard orifice based TMD system. The Abscissa (X-axis) quantifies modal response frequency while the Applicate (Z-axis) of the plot is system gain. The Ordinate (Y-axis) is the excitation force magnitude. It should be underscored that the excitation force magnitude is directly proportional to the C2 “resistance to motion” term resulting from the inherent force nonlinearity of the orifice based system. In the standard TMD system, low excitation force corresponds to low C2 “resistance to motion.” Large excitation force corresponds to large C2 “resistance to motion.” This highly nonlinear relationship is directly related to the velocity squared (V2) force dependency of the orifice mechanism.
The resulting 3-D diagram is referred to as the Hartog Domain and is characterized by two distinct zones. Zone 1 includes two “split modes” and occurs when C2 “resistance to motion” term is small. Zone 2 includes a single mode defined as the “coalesced” mode and is observed when C2 damping is large. In Zone 1, where the C2 “resistance to motion” is very low or even negligible, the lower frequency split mode responds with a phase relationship between M1 and M2 that is near 0 degrees (described as the in-phase mode). The higher frequency Zone 1 split mode responds with a phase relationship between M1 and M2 that is around 180 degrees (described as the out-of-phase mode).
As excitation force and the corresponding C2 “resistance to motion” increases, the lower and higher split modes reduce in gain and eventually coalesce into a single mode with a phase relationship around 90 degrees between M1 and M2. The emergence of the coalesced mode defines Zone 2. It is important to note that the modal phase relationships between M1 and M2 are transitional terms and in practice are almost never measured to be exactly 0.0, 180.0, or 90.0 degrees.